We investigate the effects of inverse Compton scattering by electrons and p
ositrons in the unshocked winds of rotationally-powered binary pulsars. Thi
s process can scatter low energy target photons to produce gamma rays with
energies from MeV to TeV. The binary radio pulsars PSR B1259 - 63 and PSR J
0045 - 73 are both in close eccentric orbits around bright main sequence st
ars which provide a huge density of low energy target photons. The inverse
Compton scattering process transfers momentum from the pulsar wind to the s
cattered photons, and therefore provides a drag which tends to decelerate t
he pulsar wind. We present detailed calculations of the dynamics of a pulsa
r wind which is undergoing inverse Compton scattering, showing that the dec
eleration of the wind of PSR B1259 - 63 due to 'inverse Compton drag' is sm
all, but that this process may confine the wind of PSR J0045 - 73 before it
attains pressure balance with the outflow of its companion star. We calcul
ate the spectra and light curves of the resulting inverse Compton emission
from PSR B1259 - 63 and show that if the size of the pulsar wind nebula is
comparable to the binary separation, then the gamma-ray emission from the u
nshocked wind may be detectable by atmospheric Cherenkov detectors or by th
e new generation of satellite-borne gamma-ray detectors such as INTEGRAL an
d GLAST. This mechanism may therefore provide a direct probe of the freely-
expanding regions of pulsar winds, previously thought to be invisible. (C)
2000 Elsevier Science B.V. All rights reserved. PACS. 95.30.Jx: 95.55.Ka; 9
7.60.Gb; 98.70.Rz.